An approximate solution method of plane physical nonlinear problems of stress concentration about curvilinear holes in thin plates made of a material subject to a nonlinear law of elasticity is given. The solutions are represented in the form of expansions in the small parameter mu and epsilon. The determination of the stress function F for a physically nonlinear elastic plate with a hole reduces for each approximation to the integration of nonlinear differential equations. Stress concentration about an elliptic hole is considered in zero, first, and second approximation. The coefficient of stress concentration kappa is found on the contour of the hole, depending nonlinearly on the tensile forces Rho, the ellipticity of the hole, and parameter lambda characterizing the mechanical properties of the material. Tables represent the values of the coefficient of stress concentration for various values of the parameters Rho, lambda and epsilon.